Electronic Communications in Probability

The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium

Manh Hong Duong and Julian Tugaut

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In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial differential equation describing the time evolution of the probability distribution of a particle moving under the influence of a non-convex potential, an interaction potential, a friction force and a stochastic force. Using the free-energy approach, we show that under suitable assumptions solutions of the Vlasov-Fokker-Planck equation converge to an invariant probability.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 19, 10 pp.

Received: 23 August 2017
Accepted: 5 February 2018
First available in Project Euclid: 15 March 2018

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 35B40: Asymptotic behavior of solutions
Secondary: 35K55: Nonlinear parabolic equations 60J60: Diffusion processes [See also 58J65] 60G10: Stationary processes

kinetic equation Vlasov-Fokker-Planck equation free-energy asymptotic behaviour granular media equation stochastic processes

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Duong, Manh Hong; Tugaut, Julian. The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium. Electron. Commun. Probab. 23 (2018), paper no. 19, 10 pp. doi:10.1214/18-ECP116. https://projecteuclid.org/euclid.ecp/1521079417

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